It is intended to continue work on mathematically non-trivial statistical problems of biology and health. Examples: (1) Chance mechanisms operating in living cells (and in living mammals) subjected to insults, radioactive or non-radioactive. Recent work in this direction can be exemplified by a paper, joint with Prem S. Puri, published in 1976 in PNAS. Concerned with radiation damage to cells (either low or high LET) and with the subsequent biological repair, this paper differs from earlier literature by taking into account the (practical) instantaneity of damage from multiple "hits" by "secondary" radiation particles generated by a single "primary". Methodology: stochastic clustering process. A generalization is needed. (2) Experimental designs minimizing difficulties of nonidentifiability. In order to understand the mechanisms of successions of illnesses, recoveries, other illnesses and eventually death, a variety of "survival experiments" are being performed in many laboratories. Because of the complexities of successions of "transitions" from one pathological state to another, all the feasible experimental designs involve difficulties of "nonidentifiability": the same experimental data are consistent with an infinity of different chance mechanisms. It is intended to study means of decreasing the nonidentifiability difficulties, perhaps through hypotheses of biological character. (3) Optimal methodology of screening chemical and other agents, possibly involving synergisms (cocarcinogenesis). The traditional factorial experiment methodology is unreliable both for normally distributed and for binary response variables. It is intended to search for an optimal methodology.